# Dominance

This is used in many contexts, but the general meaning is that something is uniformly better than something else. For example, consider two activities in a linear program, say $LaTeX: j$ and $LaTeX: k$, such that:
• $LaTeX: j$ has greater cost: $LaTeX: c_j \ge c_k$
• $LaTeX: j$ produces less of each requirement: $LaTeX: A_{i, j} \le A_{i, k}$ for $LaTeX: i$ such that we require $LaTeX: A_{i,*}x \ge b_i$
• $LaTeX: j$ consumes more of each resource: $LaTeX: A_{i, j} \ge A_{i, k}$ for $LaTeX: i$ such that we require $LaTeX: A_{i,*}x \le b_i$
• $LaTeX: j$ produces or consumes at the same rate of goods to be conserved: $LaTeX: A_{i, j} = A_{i, k}$ for $LaTeX: i$ such that we require $LaTeX: A_{i,*}x = b_i$
Then, activity $LaTeX: k$ dominates  activity $LaTeX: j$.